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Mathematics · 2022 · 2 marks
Differential EquationsMethods of Solving First Order, First Degree Differential Equations2 marksApplyvery short answer
CBSE 2022 · Region 3 · Set 2 · Q2
Find the general solution of the differential equation: log (dy/dx)= ax + by.
Find the general solution of the differential equation: $\displaystyle \log \left(\frac{\mathrm{dy}}{\mathrm{dx}}\right)=\mathrm{ax}+\mathrm{by}$.
Marking-scheme solution
\[\begin{aligned}
& \log \left(\frac{d y}{d x}\right)=a x+b y \\
& \frac{d y}{d x}=e^{a x+b y} \\
& \frac{d y}{d x}=e^{a x} \cdot e^{b y} \\
& \int \frac{d y}{e^{b y}}=\int e^{a x} d x \\
& \frac{-e^{-b y}}{b}=\frac{e^{a x}}{a}+C
\end{aligned}
\]
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CBSE Class 12 Mathematics past-paper question from the 2022 board exam, with the answer as CBSE’s own marking scheme gives it. Where our answers come from.